Question

How many different ways can you choose 5 cards from a shuffled deck and get exactly three aces? The order of cards doesn’t matter-only which particular 5 cards matters.

Answer 1

The total number of ways to select 5 cards from a deck of 52 cards of which 3 are aces are 4512

Explanation:

The formula to find no of ways to select is
`_(n)C_(r)= (n!)/(r!(n-r)!)`

There are in all 52 cards in a deck of which 4 are aces. So 48 cards are non ace cards.

Here

We have to select 5 cards of which 3 must be aces.

there are in all 4 aces.

To select three aces from four aces we get
`_4C_3=4`

Now we have selected three aces.

We are left to select 2 cards from the rest of the 48 cards

We get

`_4_8C_2=1128`

hence the total number of ways to select 5 cards from a deck of 52 cards of which 3 are aces are = 1128 (4) = 4512